Physics-Informed Extreme Learning Machine Applied for Eigenmode Analysis of Waveguides and Transmission Lines

In this work, we propose a physics-informed extreme learning machine (PIELM) method to identify the eigenmode field distributions of waveguides and transmission lines by solving Helmholtz partial differential equation (PDE) with initial and boundary conditions. A single-layer neural network architecture is adopted in PIELM, where the input layer parameters are initialized randomly. By embedding physics-informed constraints into the loss function, a system matrix equation can be established. Then, the output layer weights can be learned with the Moore–Penrose generalized inverse algorithm. Compared with physics-informed neural network (PINN), PIELM only uses a single-layer feedforward neural network and does not engage in an iterative optimization process utilizing backpropagation and gradient descent algorithms. As a result, the time spent on model training is reduced significantly, with the total process accelerated. Some numerical examples are presented to validate both accuracy and efficiency of PIELM method compared with PINN method in solving the eigenmode field distribution problem of waveguides and transmission lines.